You'll come across a range of toilets when visiting Kyoto, from futuristic gadget-laden loos to old-school squat style. When using squat toilets, the correct position is facing the hood, away from the door.
Public toilets are free and generally clean and well-maintained. Most convenience stores...
Kyoto is generally a very safe city and crime is rare. Use common sense and follow the same precautions you normally would.
Take care when crossing the street or exiting restaurants, hotels and shops onto the pavement; there's almost always someone on a bicycle coming your way.